A324841 Matula-Goebel numbers of fully recursively anti-transitive rooted trees.

1, 2, 3, 4, 5, 7, 8, 9, 11, 16, 17, 19, 21, 23, 25, 27, 31, 32, 35, 49, 51, 53, 57, 59, 63, 64, 67, 73, 77, 81, 83, 85, 95, 97, 103, 115, 121, 125, 127, 128, 131, 133, 147, 149, 153, 159, 161, 171, 175, 177, 187, 189, 201, 209, 217, 227, 233, 241, 243, 245

Offset

1,2

Comments

An unlabeled rooted tree is fully recursively anti-transitive if no proper terminal subtree of any terminal subtree is a branch of the larger subtree.

Links

Table of n, a(n) for n=1..60.

Example

The sequence of fully recursively anti-transitive rooted trees together with their Matula-Goebel numbers begins:
   1: o
   2: (o)
   3: ((o))
   4: (oo)
   5: (((o)))
   7: ((oo))
   8: (ooo)
   9: ((o)(o))
  11: ((((o))))
  16: (oooo)
  17: (((oo)))
  19: ((ooo))
  21: ((o)(oo))
  23: (((o)(o)))
  25: (((o))((o)))
  27: ((o)(o)(o))
  31: (((((o)))))
  32: (ooooo)
  35: (((o))(oo))
  49: ((oo)(oo))
  51: ((o)((oo)))
  53: ((oooo))
  57: ((o)(ooo))
  59: ((((oo))))
  63: ((o)(o)(oo))

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
fratQ[n_]:=And[Intersection[Union@@Rest[FixedPointList[Union@@primeMS/@#&, primeMS[n]]], primeMS[n]]=={}, And@@fratQ/@primeMS[n]];
Select[Range[100], fratQ]

Crossrefs

Cf. A000081, A007097, A290689, A303431, A304360, A306844, A316502, A318185, A318186.

Cf. A324695, A324751, A324756, A324758, A324766, A324768, A324769.

Cf. A324838, A324840, A324844.

Sequence in context: A328668 A316468 A099627 * A184155 A331913 A318612

Adjacent sequences: A324838 A324839 A324840 * A324842 A324843 A324844

Keyword

nonn

Author

Gus Wiseman, Mar 17 2019

Status

approved